Twitter has now Bookmarks allowing users to save tweets
Twitter rolled out today new actions on tweets. Users are now able to direct message tweets to others, share tweets via email or text messages, and bookmark tweets.
Bookmarks on Twitter allow users to save tweets privately. Twitter gives some examples: when users want to save something historic, don’t want to forget a joke, or saw an article to read later.
All the bookmarked tweets are not available to others.